Why are camcorders with DSLR sensors not available?

I am currently educating myself whether I want to buy a camcorder (like the Canon Vixia HF S30) or a DSLR (like the Canon T3i). There are of course several differences. However, from what I learned, the most important differences is the size of the sensor. DSLRs have sensors around 12 times as big as the ones in camcorders. The size of the sensor is responsible for the great low light ability and the shallow depth of field you can get with DSLRs.
I am wondering, why are there no (normal prized) camcorders available that have a DSLR sensor? The format of the body of a DSLRs is not great for shooting film. So, putting DSLR technology with the large sensor into a camcorder body, would make it so much better for film making. Why are there no camcorders in the price range of $800-1000 (that's what the T3i costs) available?

I have watched tons of videos and read lots of stuff but it seems no where is that being discussed.

Because a videocamera that good and that cheap would leave consumers little reason to buy their more expensive cameras. There are and will be relativly inexpensive camcorders with large chips but these cameras will be purposely hobbled by the manufacturer to give you some reason to buy one of their more expensive models

Only a manufacturer with nothing to protect would build the kind of camera you are dreaming of

That will eventually happen- but you can't have it all for so cheap. Either you get a DSLR like a T3i- which really is a massive bargain for the quality of the chip with the tradeoff that operating it as a video camera is not as ergonomic as a dedicated camcorder. Or you pony up for a proper camcorder with a DSLR like chip- such as a Panasonic AF100 or Sony F3. Sony's VG series is about as close as I've seen to what you want...

Another reason for the price is the fact that there are a lot more photographers than videographers out there, so the market for the DLSR's is a lot bigger which allows them to sell DSLR's at a lower price than traditional video cameras and still make a profit.

Camcorders and DSLRs are different rivers that have crossed just of late. Their technologies and ways of operating are very different. That's my guess. I believe you can't just stick a DSLR sensor into a camcorder without overhauling the entire video camera.

Plus DSLRs overheat after about an hour of continuous use which doesn't sit well with consumers. DSLRs are still cameras first, that happen to shoot video and is full of caveats. Canon recently revealed a 4K video camera and RED has a camera coming out that has a reasonable price point. The age of DSLRs shooting video is almost over imo, because companies are creating cameras with these nice sensors that are fully functioning motion cameras.

One more thing keeping those big sensors out of little Vixia camcorders is that they're diametrically opposed to the needs of the consumer market.

Pros like us that frequent this website generally understand how to manually focus, swap lenses, use tripods, etc. For a mass-market consumer camera to be usable with a large sensor, it would have to have a monster-sized autofocusing, image stabilized, 15x built-in zoom lens so Grandma can zoom in on the grandkids at the recital like she used to with her 8mm Handycam. Of course, a lens like that would be ridiculously cost-prohibitive for a large-format sensor on a cheap camera, but it's easy for a tiny sensor.

There's quite a few cameras doing exactly what you want, but none of them are quite that cheap because they're made for a narrow prosumer/professional audience. It's all about economies of scale, and there's not millions of customers lining up for these. Thousands, but not millions. There are millions lining up for T3i's since they're primarily a mass-market SLR which does everything automatically for Granny if she prefers. Video is just an odd bonus for tinkerers.

There is the Sony NEX-VG20, which is pretty close to what you're asking for in the first place. Just with a boatload of other compromises.